Conventionally, there has been known an engagement device which is provided with a first member having engaged teeth arranged around a rotation shaft and a second member having engaging teeth and engages the engaging teeth with the engaged teeth to engage both the members. As such an engagement device, for example, Patent Literature 1 discloses a meshing device which has inclined surfaces provided in a tooth part of a drive gear and a tooth part of a driven gear, each of the inclined surfaces being located between an end surface opposing the other gear and a tooth surface. The inclined surface of the drive gear is formed on the rear side with respect to the rotation direction of the drive gear. On the other hand, the inclined surface of the driven gear is formed on the front side with respect to the rotation direction. In the meshing device, the inclined surface of the driven gear is first brought into contact with the inclined surface of the drive gear and moved toward the drive gear along the inclined surface of the drive gear during an engagement operation. This enables the driven gear to reliably mesh with the drive gear.